Răspuns:
Explicație pas cu pas:
2) a) b₁=6 , b₂=18 ;
q = b₂/b₁ = 18/6 = 3
b₇ = b₁·q⁶ = 6·3⁶ = 2·3⁷
b₈ = b₇·q = 2·3⁸
b₁₀ = b₈·q² = 2·3¹⁰
b) b₁=2 , b₂=1 => q = b₂/b₁ = 1/2
b₇ = b₁·q⁶ = 2·(1/2⁶) = 1/32
b₈ = b₇·q = 1/32·1/2 = 1/64
b₁₀ = b₈·q² = 1/64·1/4 = 1/256
3) 3x-10 ; 5x-12 ; x²-2 termenii unei progreii aritmetice =>
5x-12 = (3x-10+x²-2)/2 =>
10x-24 = x²+3x-12 =>
x²-7x+12 = 0 =>
x₁,₂ = [7±√(49-48)]/2
x₁,₂ = (7±1)/2 => x₁ = 3 ; x₂ = 4
sau : x²-7x+12 = 0 <=>
x²-3x-4x+12 = 0 <=>
x(x-3)-4(x-3) = 0 <=>
(x-3)(x-4) = 0 => x₁ = 3 ; x₂ = 4
x₁ = 3 => progresia : -1 ; 3 ; 7 cu ratia 4
x₂ = 4 => progresia : 2 ; 8 ; 14 cu ratia 6
